Gradient estimates for parabolic systems from composite material

Estimates for Elliptic Systems from Composite Material

Global gradient estimates for degenerate parabolic equations in nonsmooth domains

Abstract. This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates for t...

Gradient estimates for a nonlinear parabolic equation under Ricci flow

Let (M,g(t)), 0 ≤ t ≤ T , be a n-dimensional complete noncompact manifold, n ≥ 2, with bounded curvatures and metric g(t) evolving by the Ricci flow ∂gij ∂t = −2Rij . We will extend the result of L. Ma and Y. Yang and prove a local gradient estimate for positive solutions of the nonlinear parabolic equation ∂u ∂t = ∆u − au log u − qu where a ∈ R is a constant and q is a smooth function on M × [...

Gradient estimates for degenerate quasi-linear parabolic equations

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients infinitesimally form bounded with respect to the Laplacian we obtain Lq-estimates for the gradients of solutions, and for the lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space var...

Research Article Interior Gradient Estimates for Nonuniformly Parabolic Equations II